SOME FIXED POINT THEOREMS IN LOCALLY CONVEX LINEAR SPACES
Sadayuki Yamamuro · Institutional Repositories DataBase (IRDB) · 1963
$\overline{G}$ if (R) $\overline{G}$ is a closed ball and $F(\partial G)\subset\overline{G}$ . It is easy to see that this theorem is valid even in the case of a completely continuous mapping $F$ of a convex closed set $\overline{G}$ contained in a locally convex linear space $E$. Altman [1] proved a more general theorem by replacing the condition (R) by (A) $\Vert F(x)-x\Vert^{2}\geqq\Vert F(x)\Vert^{2}-\Vert x\Vert^{2}$ for every $x\in\partial G$ . Therefore, in the case of the completely continuous mapping $F$ of the